The Levenshtein Word Distance has a fairly obvious use in helping spell checkers decided which words to suggest as alternatives to mis-spelled words: if the distance is low between a mis-spelled word and an actual word then it is likely that word is what the user intended to type. However, it can be used in any situation where strings of characters need to be compared, such as DNA matching.
I recently wrote an article called Should You Learn Data Structures and Algorithms?. It is primarily about the searching and sorting algorithms which many people seem to place so much emphasis on, especially in the educational sphere. My view is that the need to implement these algorithms is rare so you would be better off concentrating on learning topics which you will need on a day to day basis. However, you might need to learn at least the basics just to convince others of your prowess so I have put together a short bit of code to illustrate a couple of the best-known sorting algorithms.
I have started of with bubble sort and selection sort. Neither are very efficient but they are simple to understand and implement. In the future I will expand this project with further algorithms.
Prime numbers have been understood at least since the Ancient Greeks, and possibly since the Ancient Egyptians. In modern times their study has intensified greatly due to their usefulness, notably in encryption, and because computers enable them to be calculated to a massively higher level than could be done by hand.
It doesn't take much thought to realise that the whole area of phonetic algorithms is a minefield, and Soundex itself is rather restricted in its usefulness. In fact, after writing this implementation I came to the conclusion that it is rather mediocre but at least coding it up does give a better understanding of how it works and therefore its usefulness and limitations.
Wikipedia has a surprisingly brief article on the topic Soundex on Wikipedia which you might like to read.